To find the composite function $(g \circ f)(x)$, you need to substitute $f(x)$ into $g(x)$.

In simple terms, a composite function is formed when one function is applied to the result of another function. The notation $(g \circ f)(x)$ indicates that you first evaluate the function $f$ at $x$, and then apply the function $g$ to the outcome of $f(x)$.

Here’s a step-by-step guide on how to compute a composite function:

1. Identify the Functions: Let’s say you have two functions, $f(x)$ and $g(x)$. For instance, let $f(x) = 2x + 3$ and $g(x) = x^2$.

2. Substitute $f(x)$ into $g(x)$: In this step, you replace the variable $x$ in $g(x)$ with the entire expression from $f(x)$. For our example, this means substituting $f(x) = 2x + 3$ into $g(x) = x^2$. Therefore, we have:

   $$g(f(x)) = g(2x + 3) = (2x + 3)^2.$$

3. Simplify if Necessary: You may need to simplify the resulting expression. Continuing with our example, we can expand $(2x + 3)^2$:

   $$(2x + 3)^2 = 4x^2 + 12x + 9.$$

Thus, the composite function $(g \circ f)(x)$ for our example is

This procedure can be applied to any pair of functions to find their composite. Keep in mind that the order of composition is important: generally, $(g \circ f)(x)$ is not the same as $(f \circ g)(x)$.